Ég kaupi bók fyrir Önnu.

• Ég = the subject, I
• kaupi = the finite verb, buy / am buying
• bók = the direct object, a book
• fyrir Önnu = a prepositional phrase, for Anna

So the sentence structure is:

subject + verb + object + prepositional phrase

That is the most neutral, everyday word order here.

kaupi is the 1st person singular present tense of að kaupa (to buy).

So:

• ég kaupi = I buy
• þú kaupir = you buy
• hann/hún/það kaupir = he/she/it buys
• við kaupum = we buy
• þið kaupið = you (plural) buy
• þeir/þær/þau kaupa = they buy

A learner often meets the dictionary form að kaupa, but in a sentence with ég, you need the conjugated form kaupi.

Because Icelandic has no indefinite article.

So:

• bók = a book or just book, depending on context

If you want the book, Icelandic usually adds the definite article to the end of the noun:

• bókin = the book (nominative)
• bókina = the book (accusative)

So Ég kaupi bók literally looks like I buy book, but in natural English it means I buy a book.

bók is the accusative singular here because it is the direct object of kaupi.

The verb að kaupa normally takes an accusative object.

The reason the word still looks like bók is that for this noun, the nominative and accusative singular are the same:

• nominative: bók
• accusative: bók

So the case is there grammatically, even though the form does not change.

Because after fyrir in this meaning, the name is not in the basic nominative form. It appears in an oblique case form, and Anna changes to Önnu.

For this name:

• nominative: Anna
• accusative: Önnu
• dative: Önnu
• genitive: Önnu

So Anna is the form you use as the subject, but Önnu is the form you use in several other grammatical roles.

This is something you need to learn with the noun or name itself: Icelandic nouns and names decline.

Yes. In this sentence, fyrir is used in the sense of for / on behalf of / intended for, and in that usage it takes the accusative.

So:

• fyrir Önnu = for Anna

A small extra point: with Anna, the accusative and dative both happen to be Önnu, so the form itself does not show the difference. But grammatically, in this sentence, it is analyzed as accusative.

Here, fyrir means something like:

• for Anna
• intended for Anna
• on Anna’s behalf

In this sentence, the most natural reading is that Anna is the person the book is for.

Be aware that fyrir has several meanings in Icelandic depending on context, such as for, before, in front of, because of, and others. Prepositions in Icelandic are very important because they often control case and can shift meaning.

Yes. The Icelandic simple present often covers both:

• I buy
• I am buying

So Ég kaupi bók fyrir Önnu can work for either, depending on context.

If you want to make the ongoing action especially clear, Icelandic often uses:

• Ég er að kaupa bók fyrir Önnu = I am buying a book for Anna

So the shorter sentence is perfectly normal, but the vera að + infinitive pattern can make the progressive meaning more explicit.

The given order is the neutral one:

Ég kaupi bók fyrir Önnu.

But Icelandic does allow word order changes for emphasis, topic, or style. The important rule is that Icelandic is generally a verb-second (V2) language in main clauses.

For example, you can front another element:

• Fyrir Önnu kaupi ég bók.

That is possible, but it sounds more marked or contrastive than the neutral version.

So for a beginner, the safest pattern is the one in your sentence: subject + verb + object + other information.

Normally, you should keep ég.

Icelandic is not like Spanish or Italian, where subject pronouns are often dropped. In ordinary full sentences, Icelandic usually states the subject pronoun:

• Ég kaupi bók fyrir Önnu.

If you say just kaupi bók fyrir Önnu, it may sound incomplete unless the context is very special, such as notes, diary style, or very informal clipped speech.

So as a learner, it is best to include ég.

They are real Icelandic letters, not just optional accent marks.

• é in Ég is usually pronounced roughly like ye at the beginning of a word.
• ö in Önnu is a front rounded vowel, similar to German ö or French eu. There is no perfect English equivalent.

A rough learner-friendly approximation might be:

• Ég ≈ yeg / yeh with an Icelandic ending sound
• Önnu ≈ something like UHN-nu or EUR-nu, but neither is exact

The important point is that é and ö are separate vowel sounds in Icelandic, not just stressed versions of e and o.

That is part of the declension pattern of this particular name.

The oblique forms of Anna are:

• Önnu

So the change is not just -a → -u; the stem vowel changes too. This kind of alternation is something you simply have to learn as part of the word’s paradigm.

For practical purposes, memorize it like this:

• Anna = nominative
• Önnu = all the singular non-nominative forms you are most likely to meet

That will help you produce correct forms quickly.